×

Unified theory and strategies of survey sampling. (English) Zbl 0635.62008

North-Holland Series in Statistics and Probability, Vol. 4. Amsterdam etc.: North-Holland. XVII, 414 p.; $ 92.75; Dfl. 190.00 (1988).
This book is divided into two parts. Part A is devoted to the main theoretical foundations of sampling. In part B an extensive set of particular designs and strategies is given.
The first two chapters of part A fix the aims, the notations and some philosophical points of view related with the aims of sampling. Chapter 3 is devoted to the theory of design-based estimation. A brief account of the development of linear estimation is given. The basic ideas, related with estimation in finite population sampling are fixed and the role of the design-bias and other parameters is analyzed. Especially interval estimation is studied in a very interesting way and a clear interpretation of the links with normal-based interpretations is developed. The impact of the classical works of Neyman (1934), Horvitz- Thompson (1952), Godambe (1955) and others in the development of the theory is established and analyzed. The superpopulation approach is also studied and an extensive account of results is given. It begins with Godambe’s model (1955) and seventeen important results in this line are given.
Chapter 4 tackles the optimality of the designs and Chapter 5 the role of sufficiency, and derived concepts, in the search of optimal estimators. The search for the optimum via Rao-Blackwell method is characterized as well as the completeness. Linear sufficiency and the possibility of deducing a minimum variance strategy in the class of unbiased estimators are introduced. Posterior and relevant results in that line are also given.
Chapter 6 plays an important role in clarifying the particularities of inference in finite populations. The general concept of random experiments and its connection with a certain probability measure is the basis of statistical inference. The apparently different concepts are unified by fixing the common structure and concepts related with sampling and the corresponding parts in the general statistical theory.
The importance of artificial randomization and the discreteness of the events give a lesser importance to some general principles such as likelihood. The authors give a clear exposition of this problem. The following chapters complement this by analyzing further aspects of the likelihood and pure Bayesian together with the prediction approach. Robustness is treated in Chapter 9. An appendix is used for fixing some ideas related with optimality, robustness and other themes.
Part B is devoted to practical aspects of sampling. Firstly are developed strategies based on unequal inclusion probability sampling designs-UPS. For sample sizes equal to two a group of relevant strategies is presented.
Chapter two gives the classical results of the Horvitz-Thompson estimator-HTE, and Chapter three the ruling principles of \(\pi\) PS- sampling schemes. Chapter four develops, for \(n=2\), twelve schemes based on draw-by-draw methods, five related with the rejective method, one with grouping and the method of Narain (1951). Chapter five uses a similar structure for analyzing the general case. Seventeen draw-by-draw methods are studied, four rejective, six grouping and twelve other methods are given. HTE is used in the corresponding strategies.
Chapter six presents thirteen strategies with UPS but with different estimators and Chapter seven is devoted to the study of alternative estimators. Other estimators based on the use of auxiliary information but with equal probability sampling are presented in Chapter eight. Among them are different ratio-type estimators. Chapter nine tackles the problem of variance estimation and results on the nonnegativeness of the estimated variances of the HTE are completely reviewed.
Chapter ten analyzes alternative designs such as double sampling, sampling on successive occasions and controlled sampling. The last chapter gives comparisons between strategies using the same artificial population. An appendix develops further aspects related with Part B. A huge list of references is given.
This book fills a lack in the literature on survey sampling theory.
Reviewer: C.N.Bouza

MSC:

62D05 Sampling theory, sample surveys
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62A01 Foundations and philosophical topics in statistics
PDFBibTeX XMLCite